### Nuprl Lemma : req_weakening

`∀[a,b:ℝ].  a = b supposing a = b ∈ ℝ`

Proof

Definitions occuring in Statement :  req: `x = y` real: `ℝ` uimplies: `b supposing a` uall: `∀[x:A]. B[x]` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uimplies: `b supposing a` implies: `P `` Q` prop: `ℙ` guard: `{T}` equiv_rel: `EquivRel(T;x,y.E[x; y])` and: `P ∧ Q` refl: `Refl(T;x,y.E[x; y])` all: `∀x:A. B[x]`
Lemmas referenced :  req-equiv req_witness equal_wf real_wf and_wf req_wf
Rules used in proof :  cut introduction extract_by_obid sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation sqequalHypSubstitution isectElimination thin hypothesisEquality independent_functionElimination hypothesis sqequalRule isect_memberEquality because_Cache equalityTransitivity equalitySymmetry productElimination dependent_functionElimination hyp_replacement dependent_set_memberEquality independent_pairFormation applyEquality lambdaEquality setElimination rename setEquality

Latex:
\mforall{}[a,b:\mBbbR{}].    a  =  b  supposing  a  =  b

Date html generated: 2016_10_26-AM-09_03_17
Last ObjectModification: 2016_07_12-AM-08_13_19

Theory : reals

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