Nuprl Lemma : MachinPi4-req
MachinPi4() = (π/r(4))
Proof
Definitions occuring in Statement :
MachinPi4: MachinPi4(),
pi: π,
rdiv: (x/y),
req: x = y,
int-to-real: r(n),
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
sq_stable: SqStable(P)
Lemmas referenced :
MachinPi4_wf,
sq_stable__req,
rdiv_wf,
pi_wf,
int-to-real_wf,
rless-int,
rless_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
hypothesis,
inhabitedIsType,
lambdaFormation_alt,
thin,
setElimination,
rename,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
closedConclusion,
natural_numberEquality,
independent_isectElimination,
sqequalRule,
inrFormation_alt,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
universeIsType,
imageElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry
Latex:
MachinPi4() = (\mpi{}/r(4))
Date html generated:
2019_10_31-AM-06_05_57
Last ObjectModification:
2019_01_29-PM-03_36_38
Theory : reals_2
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