Nuprl Lemma : rmin_functionality
∀[x1,x2,y1,y2:ℝ]. (rmin(x1;y1) = rmin(x2;y2)) supposing ((x1 = x2) and (y1 = y2))
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
real: ℝ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
req-iff-bdd-diff,
rmin_wf,
req_witness,
req_wf,
real_wf,
bdd-diff_functionality,
rmin_functionality_wrt_bdd-diff,
bdd-diff_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_functionElimination,
sqequalRule,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
setElimination,
rename,
dependent_functionElimination
Latex:
\mforall{}[x1,x2,y1,y2:\mBbbR{}]. (rmin(x1;y1) = rmin(x2;y2)) supposing ((x1 = x2) and (y1 = y2))
Date html generated:
2016_05_18-AM-06_59_22
Last ObjectModification:
2015_12_28-AM-00_32_30
Theory : reals
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