### Nuprl Lemma : rsqrt-rnexp-2

`∀[x:{x:ℝ| r0 ≤ x} ]. (rsqrt(x)^2 = x)`

Proof

Definitions occuring in Statement :  rsqrt: `rsqrt(x)` rleq: `x ≤ y` rnexp: `x^k1` req: `x = y` int-to-real: `r(n)` real: `ℝ` uall: `∀[x:A]. B[x]` set: `{x:A| B[x]} ` natural_number: `\$n`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` nat: `ℕ` le: `A ≤ B` and: `P ∧ Q` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` prop: `ℙ` subtype_rel: `A ⊆r B` so_lambda: `λ2x.t[x]` so_apply: `x[s]` all: `∀x:A. B[x]` bool: `𝔹` unit: `Unit` it: `⋅` btrue: `tt` ifthenelse: `if b then t else f fi ` uiff: `uiff(P;Q)` uimplies: `b supposing a` bfalse: `ff` exists: `∃x:A. B[x]` or: `P ∨ Q` sq_type: `SQType(T)` guard: `{T}` bnot: `¬bb` assert: `↑b` true: `True` subtract: `n - m` eq_int: `(i =z j)` nequal: `a ≠ b ∈ T ` satisfiable_int_formula: `satisfiable_int_formula(fmla)` top: `Top` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  req_witness rnexp_wf false_wf le_wf rsqrt_wf rleq_wf int-to-real_wf real_wf req_wf rmul_wf set_wf eq_int_wf bool_wf eqtt_to_assert assert_of_eq_int eqff_to_assert equal_wf bool_cases_sqequal subtype_base_sq bool_subtype_base assert-bnot neg_assert_of_eq_int int_subtype_base subtract_wf satisfiable-full-omega-tt intformnot_wf intformeq_wf itermConstant_wf int_formula_prop_not_lemma int_formula_prop_eq_lemma int_term_value_constant_lemma int_formula_prop_wf req_functionality rnexp_unroll req_weakening rmul_functionality rsqrt_squared
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut extract_by_obid sqequalHypSubstitution isectElimination thin dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis hypothesisEquality setElimination rename applyEquality lambdaEquality setEquality productEquality because_Cache independent_functionElimination unionElimination equalityElimination productElimination independent_isectElimination equalityTransitivity equalitySymmetry dependent_pairFormation promote_hyp dependent_functionElimination instantiate cumulativity voidElimination intEquality isect_memberEquality voidEquality computeAll

Latex:
\mforall{}[x:\{x:\mBbbR{}|  r0  \mleq{}  x\}  ].  (rsqrt(x)\^{}2  =  x)

Date html generated: 2017_10_03-AM-10_42_46
Last ObjectModification: 2017_07_28-AM-08_18_00

Theory : reals

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