### Nuprl Lemma : rsqrt_functionality

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

Proof

Definitions occuring in Statement :  rsqrt: `rsqrt(x)` rleq: `x ≤ y` req: `x = y` int-to-real: `r(n)` real: `ℝ` uimplies: `b supposing a` 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` uimplies: `b supposing a` rsqrt: `rsqrt(x)` subtype_rel: `A ⊆r B` and: `P ∧ Q` prop: `ℙ` guard: `{T}` implies: `P `` Q` so_lambda: `λ2x.t[x]` so_apply: `x[s]` int_upper: `{i...}` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` all: `∀x:A. B[x]` uiff: `uiff(P;Q)` rev_uimplies: `rev_uimplies(P;Q)`
Lemmas referenced :  req_witness rsqrt_wf real_wf and_wf rleq_wf int-to-real_wf req_wf rmul_wf rleq_transitivity rleq_weakening set_wf rroot_wf false_wf le_wf subtype_rel_sets assert_wf isEven_wf req_weakening req_functionality rroot_functionality
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality hypothesis applyEquality lambdaEquality setElimination rename setEquality natural_numberEquality sqequalRule dependent_set_memberEquality independent_isectElimination because_Cache independent_functionElimination isect_memberEquality equalityTransitivity equalitySymmetry independent_pairFormation lambdaFormation functionEquality productElimination

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

Date html generated: 2016_05_18-AM-09_43_07
Last ObjectModification: 2015_12_27-PM-11_16_07

Theory : reals

Home Index