Nuprl Lemma : assert-rceq
∀[k:ℕ]. ∀[a,b:ℚCube(k)]. uiff(↑rceq(k;a;b);a = b ∈ ℚCube(k))
Proof
Definitions occuring in Statement :
rceq: rceq(k;a;b),
rational-cube: ℚCube(k),
nat: ℕ,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
rev_uimplies: rev_uimplies(P;Q),
eqof: eqof(d),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
deq: EqDecider(T),
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
implies: P ⇒ Q,
all: ∀x:A. B[x],
rceq: rceq(k;a;b),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-nat,
rceq_wf,
assert_witness,
rational-cube_wf,
safe-assert-deq,
istype-assert,
rc-deq_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
universeIsType,
isectIsTypeImplies,
axiomEquality,
isect_memberEquality_alt,
independent_pairEquality,
equalityIstype,
because_Cache,
independent_isectElimination,
applyEquality,
independent_functionElimination,
productElimination,
dependent_functionElimination,
rename,
setElimination,
independent_pairFormation,
lambdaFormation_alt,
inhabitedIsType,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[k:\mBbbN{}]. \mforall{}[a,b:\mBbbQ{}Cube(k)]. uiff(\muparrow{}rceq(k;a;b);a = b)
Date html generated:
2019_10_29-AM-07_49_21
Last ObjectModification:
2019_10_28-AM-11_02_00
Theory : rationals
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