Nuprl Lemma : req-equiv
EquivRel(ℝ;x,y.x = y)
Proof
Definitions occuring in Statement :
req: x = y,
real: ℝ,
equiv_rel: EquivRel(T;x,y.E[x; y])
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
real: ℝ,
so_lambda: λ2x y.t[x; y],
prop: ℙ,
so_apply: x[s1;s2],
uimplies: b supposing a,
subtype_rel: A ⊆r B,
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
real_wf,
req_wf,
bdd-diff_wf,
equiv_rel_subtype,
nat_plus_wf,
bdd-diff-equiv,
equiv_rel_functionality_wrt_iff,
iff_weakening_uiff,
req-iff-bdd-diff
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
lemma_by_obid,
hypothesis,
lambdaEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
because_Cache,
functionEquality,
intEquality,
sqequalRule,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
productElimination
Latex:
EquivRel(\mBbbR{};x,y.x = y)
Date html generated:
2016_05_18-AM-06_50_26
Last ObjectModification:
2015_12_28-AM-00_29_04
Theory : reals
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