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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